Geodesic
A sign preserving mixed finite element approximation for contact problems
International Journal of Applied Mathematics and Computer Science, Tome 21 (2011) no. 3, pp. 487-498.

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This paper is concerned with the frictionless unilateral contact problem (i.e., a Signorini problem with the elasticity operator). We consider a mixed finite element method in which the unknowns are the displacement field and the contact pressure. The particularity of the method is that it furnishes a normal displacement field and a contact pressure satisfying the sign conditions of the continuous problem. The a priori error analysis of the method is closely linked with the study of a specific positivity preserving operator of averaging type which differs from the one of Chen and Nochetto. We show that this method is convergent and satisfies the same a priori error estimates as the standard approach in which the approximated contact pressure satisfies only a weak sign condition. Finally we perform some computations to illustrate and compare the sign preserving method with the standard approach.
Keywords: variational inequality, positive operator, averaging operator, contact problem, Signorini problem, mixed finite element method
Mots-clés : nierówność wariacyjna, zagadnienie kontaktowe, metoda elementów skończonych 
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Hild, P. A sign preserving mixed finite element approximation for contact problems. International Journal of Applied Mathematics and Computer Science, Tome 21 (2011) no. 3, pp. 487-498. http://geodesic.mathdoc.fr/item/IJAMCS_2011_21_3_a6/

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